格罗弗在分段完全图上的量子行走。

IF 3.7 3区综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI:10.1098/rsta.2024.0419

Gamal Mograby, Benjamin Maloy, Anastasiia Minenkova

{"title":"格罗弗在分段完全图上的量子行走。","authors":"Gamal Mograby, Benjamin Maloy, Anastasiia Minenkova","doi":"10.1098/rsta.2024.0419","DOIUrl":null,"url":null,"abstract":"We study Grover's quantum walk on a new class of graphs, termed segmented complete graphs, which combine high symmetry with detailed spectral properties. Using these graphs, we implement Grover's search algorithm and investigate its performance, focussing on the relationship between graph volume, optimal search time and success probabilities. Our results generalize classical findings for directed weighted graphs and provide new insights into enhancing quantum search algorithms on complex graph structures.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240419"},"PeriodicalIF":3.7000,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Grover's quantum walk on segmented complete graphs.\",\"authors\":\"Gamal Mograby, Benjamin Maloy, Anastasiia Minenkova\",\"doi\":\"10.1098/rsta.2024.0419\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study Grover's quantum walk on a new class of graphs, termed segmented complete graphs, which combine high symmetry with detailed spectral properties. Using these graphs, we implement Grover's search algorithm and investigate its performance, focussing on the relationship between graph volume, optimal search time and success probabilities. Our results generalize classical findings for directed weighted graphs and provide new insights into enhancing quantum search algorithms on complex graph structures.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.\",\"PeriodicalId\":19879,\"journal\":{\"name\":\"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences\",\"volume\":\"383 2306\",\"pages\":\"20240419\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2025-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://doi.org/10.1098/rsta.2024.0419\",\"RegionNum\":3,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.1098/rsta.2024.0419","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了一类新的图上的Grover量子行走，称为分段完全图，它结合了高对称性和详细的谱性质。利用这些图，我们实现了Grover搜索算法并研究了其性能，重点研究了图量、最优搜索时间和成功概率之间的关系。我们的研究结果推广了有向加权图的经典发现，并为增强复杂图结构上的量子搜索算法提供了新的见解。本文是专题“数值分析、谱图理论、正交多项式和量子算法”的一部分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Grover's quantum walk on segmented complete graphs.

We study Grover's quantum walk on a new class of graphs, termed segmented complete graphs, which combine high symmetry with detailed spectral properties. Using these graphs, we implement Grover's search algorithm and investigate its performance, focussing on the relationship between graph volume, optimal search time and success probabilities. Our results generalize classical findings for directed weighted graphs and provide new insights into enhancing quantum search algorithms on complex graph structures.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 综合性期刊-综合性期刊

CiteScore

9.30

自引率

2.00%

发文量

367

审稿时长

3 months

期刊介绍： Continuing its long history of influential scientific publishing, Philosophical Transactions A publishes high-quality theme issues on topics of current importance and general interest within the physical, mathematical and engineering sciences, guest-edited by leading authorities and comprising new research, reviews and opinions from prominent researchers.